ABSTRACT
Understanding the asymptotic behavior of a dynamical system when system parameters are varied remains a key challenge in nonlinear dynamics. We explore the dynamics of a multistable dynamical system (the response) coupled unidirectionally to a chaotic drive. In the absence of coupling, the dynamics of the response system consists of simple attractors, namely, fixed points and periodic orbits, and there could be chaotic motion depending on system parameters. Importantly, the boundaries of the basins of attraction for these attractors are all smooth. When the drive is coupled to the response, the entire dynamics becomes chaotic: distinct multistable chaos and bistable chaos are observed. In both cases, we observe a mixture of synchronous and desynchronous states and a mixture of synchronous states only. The response system displays a much richer, complex dynamics. We describe and analyze the corresponding basins of attraction using the required criteria. Riddled and intermingled structures are revealed.
ABSTRACT
Biological neurons exposed to an external electric field can induce polarization and charge fluctuation. Indeed, the exchange of calcium, sodium and potassium ions across the cell membrane can induce an electric field as a result of a time-varying electromagnetic field set up. This field could further modulate the cell electrical activity by inducing multiple firing modes. Based on the physical law of electric field, an improved model which includes an additive electrical field variable is constructed for a network of neurons to study wave propagation and mode transition by exploring the longtime dynamics of slightly perturbed plane waves in the network. Wave pattern and mode transition dependence on the different parameters of external electric field are discussed. It is found that the plane wave propagating in the coupled system breaks down to localized structures under the activation of modulational instability. The network under high-low external electric field supports bursting synchronization. This could be a fruitful avenue to discern the occurrence of paroxysmal epilepsy.
ABSTRACT
Four nanostructured active semiconducting materials currently used in electronic inks have been structurally characterised using a combination of small angle scattering techniques and scanning electron microscopy. The percolation theory and scaling laws have been used to obtain quantitative correlations of the network topologies and the local micro-structures with the electronic and electrical properties of the printed, electronic devices. The small angle light scattering has been used to expand the lower q-range of the Ultra Small Angle x-ray Scattering curves of the 2503 metallurgical grade silicon (mSi), silicon dioxide (SiO2), aluminium dioxide (Al2O3) and titanium dioxide (TiO2) materials by close to an order of magnitude, thereby providing valuable clustering properties for each material. Each scattering curve presented a series of multiple structural levels, which are then quantified using the Unified power-law approach to provide valuable clustering characteristics such as the degree of aggregation, polydispersity and geometry standard deviation. Subsequently, a fully screen-printed field effect transistor that uses mSi as the active material is demonstrated. The transistor had an ON/OFF current-ratio of 104; an electron mobility of 0.7 cm2/V s; a leakage current in the order of 5 × 10-9 A, and no current saturation.
